Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20299603 | C2 | semidirect |
| 2. C2×#16813687 | C2 | semidirect |
| 3. #20299534 | C2 | semidirect |
| 11. #16813619 | C4 | semidirect |
| 12. #16813611 | C4 | semidirect |
| 16. C4⋊Q8×C113 | C4 | semidirect |
| 21. C4×#90673 | D4 | semidirect |
| 72. C113 | #1963 | semidirect |
| 79. C4⋊Q8 | #90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299603 | 2 |
| C2×#16813687 | 2 |
| #20299534 | 2 |
| #20299149 | 2 |
| #1963 | 113 |